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Please help with this level curveby ronho1234
Tags: curve 
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#1
Apr2212, 12:54 AM

P: 34

sketch the level curve z=(x^22y+6)/(3x^2+y) at heights z=0 and z=1
i have already compute the 2 equations for the 2 z values and drawn it in 2d but when it comes to plotting it with the extra z axis i don't know what to do. please help... 


#2
Apr2212, 12:09 PM

P: 169

As your title suggests, what you need is a 'level curve', not a level surface.
Maybe I'm wrong, but if I had to do this exercise, I'd find y(x) for z=1 and z=0 and draw them, as you say have done already. I think you're done already. 


#3
Apr2212, 02:38 PM

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There is no "extra zaxis". There is no zaxis at all! The level curves you are asked to draw are in the xyplane. Graph [itex](x^22y+6)/(3x^2+y)= 0[/itex] and [itex](x^22y+6)/(3x^2+y)= 1[/itex].
The first is easy it is the same as the graph of [itex]x^2 2y+ 6= 0[/itex] which is just the parabola [itex]y= (1/2)x^2+ 3[/itex]. The second is not much harder: [itex]x^2 2y+ 6= 4x^2+ y[/itex] or [itex]y= 6 3x^2[/itex], also a parabola. 


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